非均匀悬移质泥沙弥散速度本构方程
|
摘要
天然河流中泥沙由非均匀颗粒组成,泥沙的非均匀性对于水沙运动和河床演变过程具有重要影响。然而目前非均匀悬移质泥沙研究中很少考虑不同粒径颗粒相互作用,颗粒相互作用对非均匀沙悬浮的贡献仍不明确。本文旨在建立非均匀悬移质泥沙弥散速度本构方程,其可反映非均匀泥沙悬浮的主要力学机制。首先,基于固液两相流理论,建立非均匀沙挟沙水流的两相流方程,充分考虑不同粒径颗粒相互作用力,并推导挟沙水流两相浑水方程以避免相间作用耦合复杂的问题。其次,为封闭两相浑水方程,引入弥散速度的概念,建立非均匀沙各粒径组弥散速度本构方程,揭示非均匀沙悬浮本质上是浑水紊动、颗粒自身作用、其他粒径颗粒作用三种作用共同影响的结果。最后,基于非均匀沙弥散速度本构方程得到非均匀悬移质泥沙的输沙方程,分析非均匀沙浓度垂线分布规律,将其应用于明渠恒定均匀流中,计算的非均匀沙浓度垂线分布与实验数据能较好地吻合。相对于均匀沙公式,在浓度相对较高、粒径差异大的条件下,非均匀沙公式的计算值与实验值符合得更好,进一步验证了非均匀沙弥散速度本构方程能够从力学本质上反映不同粒径颗粒相互作用对颗粒悬浮的影响机制。
In natural rivers, suspended sediment is generally non-uniform in grain sizes, and the nonuniformity is a major factor in sediment transport and fluvial processes. However, previous studies on nonuniform sediment transport lack attention on the interactions between different grain sizes, and the nonuniformity effect on sediment suspension remains unclear. To elucidate this effect, this paper presents a constitutive equation for the drift velocity of non-uniform suspended sediment. First, applying the twophase flow theory, we develop basic governing equations of flows and non-uniform sediment transport,focusing on the particle-particle interactions between sediment groups of different grain sizes, and derive two-phase mixture equations for non-uniform sediment-laden flows that can be used to save complicated calculation of interphase interactions. Then, drift velocity is introduced for closure of the two-phase mixture equations, and its constitutive equation is developed to describe the fact that the suspension of non-uniform sediment is attributed to influences imposed by flow turbulence, sediment particles themselves, and more importantly, interaction between particles in different grain sizes. This fact distinguishes the non-uniform sediment transport from the uniform one. Finally, we construct transport equations for non-uniform sediment using this constitutive equation, and obtain vertical concentration profiles for each grain size of the mixture. Comparison of these profiles with measurements shows a good agreement, and we demonstrate the difference from the uniform sediment cases through comparing the profiles to those calculated using Rouse formula. Result shows that when the concentration is higher and the disparity in grain sizes wider,the difference in the vertical profiles between the uniform and non-uniform methods becomes more distinct,and particle-particle interactions play a more important part in sediment suspension. The constitutive equation of drift velocity provides a theoretical way to elucidate the essence and effect of particle-particle interactions on suspension of non-uniform sediment.
In natural rivers, suspended sediment is generally non-uniform in grain sizes, and the nonuniformity is a major factor in sediment transport and fluvial processes. However, previous studies on nonuniform sediment transport lack attention on the interactions between different grain sizes, and the nonuniformity effect on sediment suspension remains unclear. To elucidate this effect, this paper presents a constitutive equation for the drift velocity of non-uniform suspended sediment. First, applying the twophase flow theory, we develop basic governing equations of flows and non-uniform sediment transport,focusing on the particle-particle interactions between sediment groups of different grain sizes, and derive two-phase mixture equations for non-uniform sediment-laden flows that can be used to save complicated calculation of interphase interactions. Then, drift velocity is introduced for closure of the two-phase mixture equations, and its constitutive equation is developed to describe the fact that the suspension of non-uniform sediment is attributed to influences imposed by flow turbulence, sediment particles themselves, and more importantly, interaction between particles in different grain sizes. This fact distinguishes the non-uniform sediment transport from the uniform one. Finally, we construct transport equations for non-uniform sediment using this constitutive equation, and obtain vertical concentration profiles for each grain size of the mixture. Comparison of these profiles with measurements shows a good agreement, and we demonstrate the difference from the uniform sediment cases through comparing the profiles to those calculated using Rouse formula. Result shows that when the concentration is higher and the disparity in grain sizes wider,the difference in the vertical profiles between the uniform and non-uniform methods becomes more distinct,and particle-particle interactions play a more important part in sediment suspension. The constitutive equation of drift velocity provides a theoretical way to elucidate the essence and effect of particle-particle interactions on suspension of non-uniform sediment.
引文
[1]PARKER G.Selective sorting and abrasion of river gravel.I:Theory[J].Journal of Hydraulic Engineering,1991,117(2):131-147.
[2]WILCOCK P R,CROWE J C.Surface-based transport model for mixed-size sediment[J].Journal of Hydraulic Engineering,2003,129(2):120-128.
[3]WU W M,WANG S S Y,JIA Y.Nonuniform sediment transport in alluvial rivers[J].Journal of Hydraulic Research,2000,38(6):427-434.
[4]GUO Q C,JIN Y C.Modeling nonuniform suspended sediment transport in alluvial rivers[J].Journal of Hydraulic Engineering,2002,128(9):839-847.
[5]韩其为.非均匀悬移质不平衡输沙[M].北京:科学出版社,2013.HAN Qiwei.Non-equilibrium transport of non-uniform suspended load[M].Beijing:Science Press,2013.(in Chinese)
[6]QIAN H L,CAO Z X,PENDER G,et al.Well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers[J].International Journal of Sediment Research,2015,30(2):117-130.
[7]ARMANINI A,DI SILVIO G.A one-dimensional model for the transport of a sediment mixture in non-equilibrium conditions[J].Journal of Hydraulic Research,1988,26(3):275-292.
[8]吴保生,马吉星.床沙代表粒径与输移泥沙中值粒径的关系[J].泥沙研究,2002,4(2):6-14.WU Baosheng,MA Jixing.Representative diameter of bed material and median size of sediment in transport[J].Journal of Sediment Research,2002,4(2):6-14.(in Chinese)
[9]何文社.非均匀沙运动特性研究[D].成都:四川大学,2002.HE Wenshe.Study on laws of transport for non-uniform sediment[D].Chengdu:Sichuan University.2002.(in Chinese)
[10]WU B S,MOLINAS A,JULIEN P Y.Bed-material load computations for nonuniform sediments[J].Journal of Hydraulic Engineering,2004,130(10):1002-1012.
[11]宋佳苑.长江口非均匀沙沉速研究[D].杭州:浙江大学,2015.SONG Jiayuan.Settling velocity of non-uniform sediment in Yangtze Estuary[D].Hangzhou:Zhejiang University,2015.(in Chinese)
[12]KARIM M F,KENNEDY J F.Velocity and sedimentconcentration profiles in river flows[J].Journal of Hydraulic Engineering,1987,113(2):159-176.
[13]胡海明,李义天.非均匀沙的运动机理及输沙率计算方法的研究[J].水动力学研究与进展(A辑),1996,11(3):284-292.HU Haiming,LI Yitian.Study on mechanism of nonuniform sediment motion and computation method of transport rate[J].Journal of Hydrodynamics(Ser.A),1996,11(3):284-292.(in Chinese)
[14]JHA S K,BOMBARDELLI F A.Theoretical/numerical model for the transport of non-uniform suspended sediment in open channels[J].Advances in Water Resources,2011,34(5):577-591.
[15]张小峰,谈广鸣.非均匀沙含沙量沿垂线分布特征[J].水利学报,1992(10):48-52.ZHANG Xiaofeng,TAN Guangming.Characteristics of vertical concentration distribution of non-uniform particles[J].Journal of Hydraulic Engineering,1992(10):48-52.(in Chinese)
[16]孙志林,张超凡,杜利华,等.非均匀悬移质输沙率[J].水利学报,2016,47(4):501-508.SUN Zhilin,ZHANG Chaofan,DU Lihua,et al.Transport rate of nonuniform suspended load[J].Journal of Hydraulic Engineering,2016,47(4):501-508.(in Chinese)
[17]SHEN H W,RAO C X.Transport of uniform and nonuniform sediment sizes[C]//Proceedings of the Fifth Federal Interagency Sedimentation Conference.1991,1:162-169.
[18]钟德钰,王光谦,吴保生.泥沙运动的动理学理论[M].北京:科学出版社,2015.ZHONG Deyu,WANG Guangqian,WU Baosheng.Kinetic theory for sediment transport[M].Beijing:Science Press,2015.(in Chinese)
[19]GIBBS J W.Elementary principles in statistical mechanics[M].New Haven:Yale University Press,1902.
[20]HSU T J,JENKINS J T,LIU P L F.On two-phase sediment transport:Dilute flow[J].Journal of Geophysical Research:Oceans,2003,108(C3):3057.
[21]ZHONG D Y,WANG G Q,WU B S.Drift velocity of suspended sediment in turbulent open channel flows[J].Journal of Hydraulic Engineering,2014,140(1):35-47.
[22]GERA D,SYAMLAL M,O'BRIEN T J.Hydrodynamics of particle segregation in fluidized beds[J].International Journal of Multiphase Flow,2004,30(4):419-428.
[23]ROGERS C B,EATON J K.The behavior of solid particles in a vertical turbulent boundary layer in air[J].International Journal of Multiphase Flow,1990,16(5):819-834.
[24]张磊.颗粒惯性对挟沙水流运动的影响机理[D].北京:清华大学,2015.ZHANG Lei.Effect of particle inertia on sediment-laden flows[D].Beijing:Tsinghua University,2015.(in Chinese)
[25]ARASTOOPOUR H,WANG C H,WEIL S A.Particleparticle interaction force in a dilute gas-solid system[J].Chemical Engineering Science,1982,37(9):1379-1386.
[26]SYAMLAL M.The particle-particle drag term in a multiparticle model of fluidization[R].EG and GWashington Analytical Services Center,Inc.,Morgantown,WV(USA),1987.
[27]CAO Z X,WEI L Y,XIE J H.Sediment-laden flow in open channels from two-phase flow viewpoint[J].Journal of Hydraulic Engineering,1995,121(10):725-735.
[28]LIANG L X,YU X P,BOMBARDELLI F.A general mixture model for sediment laden flows[J].Advances in Water Resources,2017,107:108-125.
[29]ISHII M,HIBIKI T.Thermo-fluid dynamics of two-phase flow[M].New York:Springer,2006.
[30]DRUZHININ O A.Dynamics of concentration and vorticity modification in a cellular flow laden with solid heavy particles[J].Physics of Fluids,1995,7(9):2132-2142.
[31]LYN D A.A similarity approach to turbulent sedimentladen flows in open channels[J].Journal of Fluid Mechanics,1988,193:1-26.
[32]GREIMANN B P,HOLLY F M.Two-phase flow analysis of concentration profiles[J].Journal of Hydraulic Engineering,2001,127(9):753-762.
[33]ENWALD H,PEIRANO E,ALMSTEDT A E.Eulerian two-phase flow theory applied to fluidization[J].International Journal of Multiphase Flow,1996,22:21-66.
[34]GIDASPOW D.Multiphase flow and fluidization:continuum and kinetic theory descriptions[M].London:Academic Press,1994.
[35]OLIVEIRA P J,ISSA R I.Numerical aspects of an algorithm for the Eulerian simulation of two-phase flows[J].International Journal for Numerical Methods in Fluids,2003,43(10):1177-1198.
[36]CSANADY G T.Turbulent diffusion of heavy particles in the atmosphere[J].Journal of the Atmospheric Sciences,1963,20(3):201-208.
[37]JULIEN P Y.Erosion and sedimentation[M].Cambridge:Cambridge University Press,1995.
[38]RICHARDSON J F,ZAKI W N.The sedimentation of a suspension of uniform spheres under conditions of viscous flow[J].Chemical Engineering Science,1954,3(2):65-73.
[39]张瑞瑾.河流泥沙动力学[M].北京:中国水利水电出版社,1998.ZHANG Ruijin.River sediment dynamics[M].Beijing:China Water&Power Press,1998.
[40]TAGGART W C,IPPEN A T,MONTES J S,et al.Effects of sediment size and gradation on concentration profiles for turbulent flow[M].Ralph M.Parsons Laboratory for Water Resources and Hydrodynamics,1972.
[41]ROUSE H.Modern conceptions of the mechanics or fluid turbulence[J].Transactions of the American Society of Civil Engineers,1937,102(1):436-507.
[2]WILCOCK P R,CROWE J C.Surface-based transport model for mixed-size sediment[J].Journal of Hydraulic Engineering,2003,129(2):120-128.
[3]WU W M,WANG S S Y,JIA Y.Nonuniform sediment transport in alluvial rivers[J].Journal of Hydraulic Research,2000,38(6):427-434.
[4]GUO Q C,JIN Y C.Modeling nonuniform suspended sediment transport in alluvial rivers[J].Journal of Hydraulic Engineering,2002,128(9):839-847.
[5]韩其为.非均匀悬移质不平衡输沙[M].北京:科学出版社,2013.HAN Qiwei.Non-equilibrium transport of non-uniform suspended load[M].Beijing:Science Press,2013.(in Chinese)
[6]QIAN H L,CAO Z X,PENDER G,et al.Well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers[J].International Journal of Sediment Research,2015,30(2):117-130.
[7]ARMANINI A,DI SILVIO G.A one-dimensional model for the transport of a sediment mixture in non-equilibrium conditions[J].Journal of Hydraulic Research,1988,26(3):275-292.
[8]吴保生,马吉星.床沙代表粒径与输移泥沙中值粒径的关系[J].泥沙研究,2002,4(2):6-14.WU Baosheng,MA Jixing.Representative diameter of bed material and median size of sediment in transport[J].Journal of Sediment Research,2002,4(2):6-14.(in Chinese)
[9]何文社.非均匀沙运动特性研究[D].成都:四川大学,2002.HE Wenshe.Study on laws of transport for non-uniform sediment[D].Chengdu:Sichuan University.2002.(in Chinese)
[10]WU B S,MOLINAS A,JULIEN P Y.Bed-material load computations for nonuniform sediments[J].Journal of Hydraulic Engineering,2004,130(10):1002-1012.
[11]宋佳苑.长江口非均匀沙沉速研究[D].杭州:浙江大学,2015.SONG Jiayuan.Settling velocity of non-uniform sediment in Yangtze Estuary[D].Hangzhou:Zhejiang University,2015.(in Chinese)
[12]KARIM M F,KENNEDY J F.Velocity and sedimentconcentration profiles in river flows[J].Journal of Hydraulic Engineering,1987,113(2):159-176.
[13]胡海明,李义天.非均匀沙的运动机理及输沙率计算方法的研究[J].水动力学研究与进展(A辑),1996,11(3):284-292.HU Haiming,LI Yitian.Study on mechanism of nonuniform sediment motion and computation method of transport rate[J].Journal of Hydrodynamics(Ser.A),1996,11(3):284-292.(in Chinese)
[14]JHA S K,BOMBARDELLI F A.Theoretical/numerical model for the transport of non-uniform suspended sediment in open channels[J].Advances in Water Resources,2011,34(5):577-591.
[15]张小峰,谈广鸣.非均匀沙含沙量沿垂线分布特征[J].水利学报,1992(10):48-52.ZHANG Xiaofeng,TAN Guangming.Characteristics of vertical concentration distribution of non-uniform particles[J].Journal of Hydraulic Engineering,1992(10):48-52.(in Chinese)
[16]孙志林,张超凡,杜利华,等.非均匀悬移质输沙率[J].水利学报,2016,47(4):501-508.SUN Zhilin,ZHANG Chaofan,DU Lihua,et al.Transport rate of nonuniform suspended load[J].Journal of Hydraulic Engineering,2016,47(4):501-508.(in Chinese)
[17]SHEN H W,RAO C X.Transport of uniform and nonuniform sediment sizes[C]//Proceedings of the Fifth Federal Interagency Sedimentation Conference.1991,1:162-169.
[18]钟德钰,王光谦,吴保生.泥沙运动的动理学理论[M].北京:科学出版社,2015.ZHONG Deyu,WANG Guangqian,WU Baosheng.Kinetic theory for sediment transport[M].Beijing:Science Press,2015.(in Chinese)
[19]GIBBS J W.Elementary principles in statistical mechanics[M].New Haven:Yale University Press,1902.
[20]HSU T J,JENKINS J T,LIU P L F.On two-phase sediment transport:Dilute flow[J].Journal of Geophysical Research:Oceans,2003,108(C3):3057.
[21]ZHONG D Y,WANG G Q,WU B S.Drift velocity of suspended sediment in turbulent open channel flows[J].Journal of Hydraulic Engineering,2014,140(1):35-47.
[22]GERA D,SYAMLAL M,O'BRIEN T J.Hydrodynamics of particle segregation in fluidized beds[J].International Journal of Multiphase Flow,2004,30(4):419-428.
[23]ROGERS C B,EATON J K.The behavior of solid particles in a vertical turbulent boundary layer in air[J].International Journal of Multiphase Flow,1990,16(5):819-834.
[24]张磊.颗粒惯性对挟沙水流运动的影响机理[D].北京:清华大学,2015.ZHANG Lei.Effect of particle inertia on sediment-laden flows[D].Beijing:Tsinghua University,2015.(in Chinese)
[25]ARASTOOPOUR H,WANG C H,WEIL S A.Particleparticle interaction force in a dilute gas-solid system[J].Chemical Engineering Science,1982,37(9):1379-1386.
[26]SYAMLAL M.The particle-particle drag term in a multiparticle model of fluidization[R].EG and GWashington Analytical Services Center,Inc.,Morgantown,WV(USA),1987.
[27]CAO Z X,WEI L Y,XIE J H.Sediment-laden flow in open channels from two-phase flow viewpoint[J].Journal of Hydraulic Engineering,1995,121(10):725-735.
[28]LIANG L X,YU X P,BOMBARDELLI F.A general mixture model for sediment laden flows[J].Advances in Water Resources,2017,107:108-125.
[29]ISHII M,HIBIKI T.Thermo-fluid dynamics of two-phase flow[M].New York:Springer,2006.
[30]DRUZHININ O A.Dynamics of concentration and vorticity modification in a cellular flow laden with solid heavy particles[J].Physics of Fluids,1995,7(9):2132-2142.
[31]LYN D A.A similarity approach to turbulent sedimentladen flows in open channels[J].Journal of Fluid Mechanics,1988,193:1-26.
[32]GREIMANN B P,HOLLY F M.Two-phase flow analysis of concentration profiles[J].Journal of Hydraulic Engineering,2001,127(9):753-762.
[33]ENWALD H,PEIRANO E,ALMSTEDT A E.Eulerian two-phase flow theory applied to fluidization[J].International Journal of Multiphase Flow,1996,22:21-66.
[34]GIDASPOW D.Multiphase flow and fluidization:continuum and kinetic theory descriptions[M].London:Academic Press,1994.
[35]OLIVEIRA P J,ISSA R I.Numerical aspects of an algorithm for the Eulerian simulation of two-phase flows[J].International Journal for Numerical Methods in Fluids,2003,43(10):1177-1198.
[36]CSANADY G T.Turbulent diffusion of heavy particles in the atmosphere[J].Journal of the Atmospheric Sciences,1963,20(3):201-208.
[37]JULIEN P Y.Erosion and sedimentation[M].Cambridge:Cambridge University Press,1995.
[38]RICHARDSON J F,ZAKI W N.The sedimentation of a suspension of uniform spheres under conditions of viscous flow[J].Chemical Engineering Science,1954,3(2):65-73.
[39]张瑞瑾.河流泥沙动力学[M].北京:中国水利水电出版社,1998.ZHANG Ruijin.River sediment dynamics[M].Beijing:China Water&Power Press,1998.
[40]TAGGART W C,IPPEN A T,MONTES J S,et al.Effects of sediment size and gradation on concentration profiles for turbulent flow[M].Ralph M.Parsons Laboratory for Water Resources and Hydrodynamics,1972.
[41]ROUSE H.Modern conceptions of the mechanics or fluid turbulence[J].Transactions of the American Society of Civil Engineers,1937,102(1):436-507.